Psalm 107 is a psalm of thanksgiving, celebrating God's deliverance of his people from various hardships. Verse 12 needs to be understood in the context of the preceding verses, which describe the specific hardship being addressed in this section.

Looking at the context, verses 10-11 speak of people imprisoned in darkness and chains:

"Some sat in darkness and in the shadow of death, prisoners in affliction and in irons, for they had rebelled against the words of God, and despised the counsel of the Most High."

So, verse 12 explains why they were in this predicament and what resulted from it:

"Therefore he brought down their heart with labor." "Therefore" connects this to the preceding verses - because they rebelled against God's word and despised his counsel. God humbled them with hardship and toil. He made their hearts weary and broken. The "labor" likely refers to the toil and suffering they endured in their imprisonment and affliction.
"They fell down, and there was no one to help." "They fell down" suggests they were completely helpless, weakened by their suffering, perhaps even close to death. "And there was no one to help" emphasizes their complete isolation and dependence. Their own strength had failed them, and they had no human source of rescue.

In essence, the verse means:

Because the people rebelled against God, he humbled them by allowing them to suffer greatly. They were weakened and helpless, unable to save themselves, and no one else could rescue them. This was a consequence of their disobedience.

The theological implication is clear:

Disobedience to God leads to suffering and a sense of helplessness. It highlights the importance of heeding God's word and counsel. The verse also sets the stage for the subsequent verses (13-16), which describe how these same people cried out to God in their distress, and he delivered them. This emphasizes God's mercy and willingness to forgive and restore those who turn to him, even after experiencing the consequences of their actions.